2 A study of the students taking distance learning courses a

2. A study of the students taking distance learning courses at a university finds that they are mostly older students not living in the university town. Choose a distance learning student at random. Let A be the event that the student is 25 years old or older and B the event that the student is local. The study finds that:
P(A) = 0.7, P(B) = 0.25, and P(A and B) = 0.05.

A.	What is the probability that the student is less than 25 years old?

2. A study of the students taking distance learning courses at a university finds that they are mostly older students not living in the university town. Choose a distance learning student at random. Let A be the event that the student is 25 years old or older and B the event that the student is local. The study finds that: P(A) = 0.7, P(B) = 0.25, and P(A and B) = 0.05. What is the probability that the student is less than 25 years old? What is the probability that the student is at least 25 years old and not local?

Solution

= P(A\')
= 1 - P(A)
= 1 - 0.7
= 0.3

P(student is at least 25 and not local)
= P(A and B\')
= P(A) - P(A and B)
= 0.7 - 0.05
= 0.65